STAT 3013 HOMEWORK 6 DUE: OCT 24, 2016 1. The simple linear regression theoretical model for a response variable y and predictor variable x is y= 0 + 1 x + What is ? Why do we have it in the theoretical model? 2. What assumptions do we make about the simple linear regression model? 3. What do we conclude if we can reject H 0 : 1=0 in favor of H a : 1 0 at significance level? 1 STAT 3013 HOMEWORK 6 DUE: OCT 24, 2016 4. Suppose we are interested in modeling the relation between two variables, x and y, and our scatterplot looks like the following. Does using simple linear regression seem appropriate? Why or why not 5. What is the difference between the prediction interval and the confidence interval? 6. A study is being conducted on bandwidth usage. It seems likely that bandwidth usage can be predicted using income. A sample of 25 households is taken. The household income (in thousands of dollars) and the amount of bandwidth used (in gigabytes or GB) in the month of October are recorded for each household. A simple linear regression line is estimated using the data. If the slope for the estimated regression line is 3.99. Provide an explanation for what this number means. 2 STAT 3013 HOMEWORK 6 DUE: OCT 24, 2016 3